How to cope with an ageing population is one of the crucial economic questions of our time, but you would hardly guess it from the lack of attention it receives in the media.

From time to time we are reminded that there is a ticking demographic time bomb, but the full scale of the challenge is rarely acknowledged.

At the start of the last century, there were two million people aged over 65. Today, it is more than ten million, and it is expected to rise to nearly twenty million by 2050.

The number of people aged 75 and over is expected to double in the next twenty years, from less than five million today to nearly nine million in 2035.

The economic implications are profound. The annual healthcare costs of a person aged 85 or over are five times higher than those of somebody in their early 60s, and ten times higher than somebody in their 40s.

The extent to which ageing has necessitated the spiralling budget of the NHS in recent decades is a matter of debate, but there is no doubt that it has been an important factor.

Significant though they are, healthcare costs are a relatively small part of the costs of ageing when compared to pensions and other old age welfare payments.

When the basic state pension was introduced after the Second World War, life expectancy was 68. It is now 81 and is expected to rise to 87 in the next fifteen years. It may not be long before people spend more years of life out of work than in work.

The Office for Budget Responsibility expects increased demand for healthcare, long-term care and state pensions – mostly caused by greater longevity – to gobble up an additional five per cent of GDP by 2065.

None of this is necessarily unsustainable given a strong economy, but as the number of workers dwindles relative to the number of dependants we will be set a challenge that no society has had to confront before.

Contrast the modest amount of coverage this serious issue attracts with the claims that are routinely made about obesity ‘bankrupting the NHS’ and smokers being a ‘drain on the taxpayer’. Last year, the NHS published a report which claimed that the very sustainability of the health service required ‘hard-hitting national action on obesity, smoking, alcohol and other major health risks’.

It would appear that we are a drain on the taxpayer if we live too long and a drain on the taxpayer if we die too early. But which is really more costly?

The economic evidence strongly suggests that old age requires much more expenditure than premature mortality. Diseases related to obesity and smoking are usually, though not always, cheaper to deal with than the chronic, non-fatal diseases of old age and they are also – to put it bluntly – lethally efficient.

If anyone is a ‘drain on the taxpayer’, it those who indulge in healthy lifestyles and live to a ripe old age. Every year in old age is spent taking more in services and benefits than is paid in tax.

People will argue, quite rightly, that old people have paid into the system all their lives and deserve their benefits in retirement, but that does not change the fact that the burden on working taxpayers rises as the elderly cohort expands.

The principal aim of healthy living is to extend life. It should be no surprise, then, that most preventive health measures end up costing more than they save.

Health economists have long argued that policies designed to extend life should be promoted on the basis that better health has intrinsic benefits rather than on spurious claims about saving money.

But when the government cut the UK’s £3 billion public health budget by £200 million earlier this year, the Faculty of Public Health claimed that it would cost the NHS ‘at least £1 billion’ in the long run.

This ‘stitch in time’ theory doesn’t stand up against the facts. As I show in Death and Taxes, a new report from the Institute of Economic Affairs, it is highly unlikely that efforts to deter physical inactivity, over-eating, smoking and drinking will save the taxpayer any money.

In fact if successful, they will almost certainly require greater public spending further down the line.

This is, of course, not an argument for encouraging worse health. But the pervasive fiction that the NHS’s financial problems would be solved if we all just ate our greens and cut down on the wine encourages unrealistic expectations about the ability of public health policy to cut costs, while making scapegoats of people whose healthcare costs are actually lower than those who lead ‘healthy lifestyles’.

The reality is that life expectancy has increased largely as a result of healthier lifestyles – better nutrition and lower smoking rates, for example – and that this has led to significantly higher costs to government budgets.

The question of how to deal with the economic consequences of our grandparents in a system of state-run healthcare and welfare remains an important one. By contrast, the drinking and obesity ‘time bombs’ are paper tigers.